We adopt the multilayer perceptron (MLP) to approximate the nonlinear input-output mapping and propose the use of particle swarm optimization with mutation (MPSO) algorithm to adjust the weights in MLP. In the supervised training step, the input of the network is the apparent conductivity (Ca) and the desired output is the true formation conductivity (Ct). MLP with optimal size 10-9-10 is chosen as the model. We have experiment in simulation and real data application. In simulation, there are 31 sets of simulated well log data, where 25 sets are used for training, and 6 sets are used for testing. After training the MLP network, input Ca, then Ct' can be inverted in testing process. Also we apply it to the inversion of real field well log data. The result is acceptable. It shows that the proposed MPSO algorithm in MLP weight adjustments can perform the well log data inversion.